Using the first principle calculations, the structural, electronic and optical properties of the monolayer graphene-like MoX 2 sheet are calculated. Our results show that the chalcogenide atoms in the stability and the lattice parameters of the MoX 2 sheet have a key role, although it is known that the electronic properties are more dependent on the metal atoms in these sheets. Our data also confirm semiconductor behavior of the MoX 2 monolayers with direct band gap for S, Se and Te chalcogenides. Compared with the bulk compounds, they have similar structural properties but represent unique electronic and optical properties that can be used in nano-devices, nano-electronics and so on. In this work, the investigation of the chalcogenide atoms role in modifying the optical properties of these single-layer sheets, such as absorption and refraction coefficients, is carried out; the dielectric constant plays an important role. We also try to study the possibility of using these compounds on the solar energy industries and optical devices.